What is the integral of (sqrt(x^2-16))/(x^3) ?

The integral of (sqrt(x^2-16))/(x^3) is -(sqrt(x^2-16))/(2x^2)+1/8 arcsec(1/4 x)+C

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integral of (sqrt(x^2-16))/(x^3)

\int \frac{x ^{2} - 16}{x ^{3}} d x

- \frac{x ^{2} - 16}{2 x ^{2}} + \frac{1}{8} arcsec (\frac{1}{4} x) + C

Solution steps

\int \frac{x ^{2} - 16}{x ^{3}} d x

Apply Integration By Parts

: - \frac{x ^{2} - 16}{2 x ^{2}} - \int - \frac{1}{2 x x ^{2} - 16} d x

= - \frac{x ^{2} - 16}{2 x ^{2}} - \int - \frac{1}{2 x x ^{2} - 16} d x

\int - \frac{1}{2 x x ^{2} - 16} d x = - \frac{1}{8} arcsec (\frac{1}{4} x)

= - \frac{x ^{2} - 16}{2 x ^{2}} - (- \frac{1}{8} arcsec (\frac{1}{4} x))

Simplify

= - \frac{x ^{2} - 16}{2 x ^{2}} + \frac{1}{8} arcsec (\frac{1}{4} x)

Add a constant to the solution

= - \frac{x ^{2} - 16}{2 x ^{2}} + \frac{1}{8} arcsec (\frac{1}{4} x) + C

f (x) = \frac{2 ln ( x )}{x}, at x = 1

\frac{d}{d x} (\frac{sin ( 8 x )}{e ^{4 x}})

\frac{\partial}{\partial x} (ln (3 y^{2} - x^{3} - 3))

x \to 0 lim (\frac{5 ^{x} - 1 3 ^{x}}{x})

x \to 0 lim (x \cdot sin (\frac{1}{x}))

What is the integral of (sqrt(x^2-16))/(x^3) ?
The integral of (sqrt(x^2-16))/(x^3) is -(sqrt(x^2-16))/(2x^2)+1/8 arcsec(1/4 x)+C